Sensory information is centred. Right now, for example, my visual
system conveys to me that there's a red wall about 1 metre
ahead (among much else); it does not convey that Wolfgang
Schwarz is about 1 metre away from a red wall on 22 January 2026 at
12:04 UTC.
We can quibble over what exactly is part of the sensory information.
We can also quibble over what "sensory information" is even meant to be.
But it should be uncontroversial that we gain information from our
senses. My point is that, on any plausible way of spelling this out, the
information we receive is centred: it doesn't have parameters that fix a
unique location in space and time. If I were unsure about what time it
is or who I am, looking at the wall in front of me wouldn't help. The
underlying reason, of course, is that photoreceptors are insensitive to
differences in spatiotemporal location: they don't produce different
outputs depending on where or when they are activated by photons.
I (somewhat randomly) picked up Kripke 2011 the other day. This
is Kripke's first engagement with the problem of empty names. What
struck me is the biased selection of examples. Most of the paper is
concerned with names of fictional characters like 'Sherlock Holmes', and
Kripke only seems to consider simple utterances in which they figure as
the subject, like (1).
A somewhat appealing (albeit, to me, also somewhat obscure) view of
mathematics is the pluralist doctrine that every consistent mathematical
theory is true, insofar as it accurately describes some mathematical
structure. I want to comment on a potential worry for this view,
mentioned in (Clarke-Doane 2020): that
it has implausible consequences for logic.
A famous argument, first proposed in (Lucas 1961), supposedly shows that the
human mind has capabilities that go beyond those of any Turing machine.
In its basic form, the argument goes like this.
Let S be the set of mathematical sentences that I accept as true. S
includes the axioms of Peano Arithmetic. Let S+ be the set of sentences
entailed by S. Suppose for reductio that my mind is equivalent to a
Turing machine. Then S is computably enumerable, and S+ is a computably
axiomatizable extension of Peano Arithmetic. So Gödel's First
Incompleteness Theorem applies: there is a true sentence G that is
unprovable in S+. By going through Gödel's reasoning, I can see that G
is true. So G is in S and thereby in S+. Contradiction!